Using trigonometry, the height of new ramp is 7.83 feet approximately
8 feet.
What is trigonometry?
Trigonometry deals with "relation of sides and angles of triangle and with relevant function of any value".
According to the question,
A loading ramp 10 feet long that makes an angle of 18° with horizontal is to be replaced by one that makes an angle 12°. The diagrammatic representation given below:
In ΔABC, ∠ABC = 18°
Trigonometry ratio cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]
cos θ = [tex]\frac{x}{10}[/tex]
x = 10.cos 18°
In ΔDEF, ∠DEF = 12°
cos θ = [tex]\frac{x}{h}[/tex]
cos 12° = (10.cos 18°)/ h [h - height of the new ramp]
h = (10.cos 18°) / cos 12°
= (10 (0.66031) )/ 0.8438
= 7.8254 ≈ 7.83 feet ≈ 8 feet
Hence, the height of new ramp is 7.83 feet approximately 8 feet.
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